Locate your date picker by a class selector.This is much easier than trying to locate ids.In case you have your controls sandwiched in an update panel you have two initialize the datepicker twice.Do this
<script type="text/javascript">
$(document).ready(function () {
var prm = Sys.WebForms.PageRequestManager.getInstance();
prm.add_initializeRequest(InitializeRequest);
prm.add_endRequest(EndRequest);
// Place here the first init of the DatePicker
$('.myclass').datepicker();
});
function InitializeRequest(sender, args) { }
function EndRequest(sender, args) {
// after update occur on UpdatePanel re-init the DatePicker
$('.myclass').datepicker();
}
</script>
Markup`
<asp:TextBox ID="txtDateSearch" CssClass="myClass" runat="server" Width="150px"></asp:TextBox>
See demo files here